{fixed,round}Tools: factor out nearestMultipleShortestRepr

extract the code from fixedToStr into its own function (defined in roundTools), to be used for serializing fractional F2Dot14 angles for COLRv1 PaintRotate etc.

Lib/fontTools/misc/fixedTools.py

@@ -17,7 +17,7 @@ functions for converting between fixed-point, float and string representations.
 	The maximum value that can still fit in an F2Dot14. (1.99993896484375)
 """
 
-from .roundTools import otRound
+from .roundTools import otRound, nearestMultipleShortestRepr
 import logging
 
 log = logging.getLogger(__name__)
@@ -125,6 +125,7 @@ def fixedToStr(value, precisionBits):
 	This is pretty slow compared to the simple division used in ``fixedToFloat``.
 	Use sporadically when you need to serialize or print the fixed-point number in
 	a human-readable form.
+	It uses nearestMultipleShortestRepr under the hood.
 
 	Args:
 		value (int): The fixed-point value to convert.
@@ -133,27 +134,8 @@ def fixedToStr(value, precisionBits):
 	Returns:
 		str: A string representation of the value.
 	"""
-	if not value: return "0.0"
-
 	scale = 1 << precisionBits
-	value /= scale
-	eps = .5 / scale
-	lo = value - eps
-	hi = value + eps
-	# If the range of valid choices spans an integer, return the integer.
-	if int(lo) != int(hi):
-		return str(float(round(value)))
-	fmt = "%.8f"
-	lo = fmt % lo
-	hi = fmt % hi
-	assert len(lo) == len(hi) and lo != hi
-	for i in range(len(lo)):
-		if lo[i] != hi[i]:
-			break
-	period = lo.find('.')
-	assert period < i
-	fmt = "%%.%df" % (i - period)
-	return fmt % value
+	return nearestMultipleShortestRepr(value/scale, factor=1.0/scale)
 
 
 def strToFixed(string, precisionBits):
@@ -214,7 +196,7 @@ def floatToFixedToStr(value, precisionBits):
 	This uses the shortest decimal representation (ie. the least
 	number of fractional decimal digits) to represent the equivalent
 	fixed-point number with ``precisionBits`` fractional binary digits.
-	It uses fixedToStr under the hood.
+	It uses nearestMultipleShortestRepr under the hood.
 
 	>>> floatToFixedToStr(-0.61883544921875, precisionBits=14)
 	'-0.61884'
@@ -227,8 +209,8 @@ def floatToFixedToStr(value, precisionBits):
 		str: A string representation of the value.
 
 	"""
-	fixed = otRound(value * (1 << precisionBits))
-	return fixedToStr(fixed, precisionBits)
+	scale = 1 << precisionBits
+	return nearestMultipleShortestRepr(value, factor=1.0/scale)
 
 
 def ensureVersionIsLong(value):

Lib/fontTools/misc/roundTools.py

@@ -56,3 +56,50 @@ def roundFunc(tolerance, round=otRound):
         return round
 
     return functools.partial(maybeRound, tolerance=tolerance, round=round)
+
+
+def nearestMultipleShortestRepr(value: float, factor: float) -> str:
+    """Round to nearest multiple of factor and return shortest decimal representation.
+
+    This chooses the float that is closer to a multiple of the given factor while
+    having the shortest decimal representation (the least number of fractional decimal
+    digits).
+
+    For example, given the following:
+
+    >>> nearestMultipleShortestRepr(-0.61883544921875, 1.0/(1<<14))
+    '-0.61884'
+
+    Useful when you need to serialize or print a fixed-point number (or multiples
+    thereof, such as F2Dot14 fractions of 180 degrees in COLRv1 PaintRotate) in
+    a human-readable form.
+
+    Args:
+        value (value): The value to be rounded and serialized.
+        factor (float): The value which the result is a close multiple of.
+
+    Returns:
+        str: A compact string representation of the value.
+    """
+    if not value:
+        return "0.0"
+
+    value = otRound(value / factor) * factor
+    eps = .5 * factor
+    lo = value - eps
+    hi = value + eps
+    # If the range of valid choices spans an integer, return the integer.
+    if int(lo) != int(hi):
+        return str(float(round(value)))
+
+    fmt = "%.8f"
+    lo = fmt % lo
+    hi = fmt % hi
+    assert len(lo) == len(hi) and lo != hi
+    for i in range(len(lo)):
+        if lo[i] != hi[i]:
+            break
+    period = lo.find('.')
+    assert period < i
+    fmt = "%%.%df" % (i - period)
+    return fmt % value